Brian earns 30 points when Brian collects 2 red gems, 2 yellow gems, and 2 blue gems,
Let r = red gems, y = yellow gem and b = blue gem.
Given that Brian earns 21 points when he collects 2 red gems and 3 yellow gems. So, we have 2r + 3y = 21 (1)
Also, he earns 31 points when he collects 2 yellow gems and 3 blue gems. So, we have
2y + 3b = 31 (2)
Finally, he earns 23 points when he collects 2 blue gems and 3 red gems. So, we have 2b + 3r = 23 (3)
From (3), b = (23 - 3r)/2
Substituting b into (2), we have
2y + 3b = 31
2y + 3(23 - 3r)/2 = 31
Expanding the bracket, we have
2y + (69 - 9r)/2 = 31
Multiplying through by 2, we have
4y + 69 - 9r = 62
4y - 9r = 62 - 69
4y - 9r = -7 (4)
So, we have two equations in y and r, which are
2r + 3y = 21 (1)
4y - 9r = -7 (4)
From (1) r = (21 - 3y)/2
substituting r into (4), we have
4y - 9(21 - 3y)/2 = -7
Expanding the bracket, we have
4y - (189 - 27y)/2 = -7
Multiplying through by 2, we have
8y -(189 - 27y) = -14
Expanding the bracket, we have
8y - 189 + 27y = -14
8y + 27y = 189 - 14
35y = 175
y = 175/35
y = 5
Substituting y = 5 into r, we have
r = (21 - 3y)/2
r = (21 - 3(5))/2
r = (21 - 15)/2
r = 6/2
r = 3
Substituting r = 3 into b, we have
b = (23 - 3r)/2
b = (23 - 3(3))/2
b = (23 - 9)/2
b = 14/2
b = 7
When Brian collects 2 red gems, 2 yellow gems, and 2 blue gems, we have
2r + 2y + 2b
substituting the values of r, y and b into the equation, we have
2r + 2y + 2b = 2 × 3 + 2 × 5 + 2 × 7
= 6 + 10 + 14
= 30 points.
So, Brian earns 30 points when Brian collects 2 red gems, 2 yellow gems, and 2 blue gems,
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Answer:
30
Step-by-step explanation:
add 21 23 and 31 up we get 75 divide that by 5 and we get 15
